Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
240 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | #6858⋊C2 |
| commutator, hypocenter | #6858 | C2×C4 |
| Frattini | C2×C33 | C2×C3⋊D3 |
| Fitting | C22×#6858 | C2 |
| socle | C22×C32 | #272 |
| prime radical | C22×C33 | C3⋊D3 |
| cosocle | C2×#6858 | C22 |
| LCS | G ▷ #6858 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #6858⋊C4 | C2 | direct (N × H) |
| 6. C2×#6858 | C4 | semidirect |
| 14. #6858 | C2×C4 | semidirect |
| 123. C2 | #6858⋊C4 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6858 | 2 |
| #6858⋊C4 | 2 |
| C2×C3⋊(3−1+2⋊C4) | 3 |
| C2×#66316 | 3 |